Patterns and Algebra Teacher Student Book – Series E Mathletics Instant Workbooks Copyright © Series E – Patterns and Algebra Contents Topic 1 –1 Patterns Section – Answers and(p. functions 1 - 21) Date completed • patterns identifying and and functions_ creating_______________________ patterns_ _________________1 / / • equations skip counting and__________________________________ equivalence_____________________ 13 / / • predicting repeating patterns_____________________ / / • predicting growing patterns_ _____________________ / / / / / / • understanding equivalence_______________________ / / • not equal to symbol_____________________________ / / • greater than and less than_ ______________________ / / • balanced equations using + and ×__________________ / / • using symbols for unknowns______________________ / / • fruit values – solve______________________________ / / • mystery snacks – solve_ _________________________ / / Section 2 – Assessment with answers (p. 22 - 27) • • • • function machines______________________________ patterns and functions_ _______________________ 22 that’s my number – apply________________________ equations and equivalence_____________________ 26 Topic 2 – Equations and equivalence Section 3 – Outcomes (p. 28 - 30) Series Author: Nicola Herringer Copyright © Patterns and functions – identifying and creating patterns Look around you, can you see a pattern? A pattern is an arrangement of shapes, numbers or colours formed according to a rule. Patterns are everywhere, you can find them in nature, art, music and even in dance! Patterns can grow or repeat depending on the rule Recognising number patterns is an important part of feeling confident in maths. In this topic we will look at different number patterns but first let’s look at shape patterns. 1 Look at these repeating shape patterns. Draw the last two shapes: a b c 2 In these repeating shape patterns, draw the missing shapes: a b 3 Complete what comes next in this growing pattern: Patterns and Algebra Copyright © 3P Learning Pty Ltd E 1 SERIES TOPIC 1 Patterns and functions – identifying and creating patterns 4 Look at these repeating shape patterns. Draw the next 2 shapes: a b c d e 5 If the patterns (above) continued, what would the 10th shape be on each row: a 6 b c d Write your name by putting each letter in the grid as a repeating pattern. For example, if your name is Ben, you would write: 1 2 3 4 5 e 1 2 3 4 5 6 7 8 9 10 B E N B E N B E N 6 7 8 9 B 10 aWhich letter of your name will be under the letter 32? b How did you work this out? Answers will vary. Patterns and Algebra Copyright © 3P Learning Pty Ltd E 1 SERIES TOPIC 2 Patterns and functions – skip counting There are many skip counting patterns to discover on a hundred grid. 1 Colour the skip counting pattern on each hundred grid: bShow the 3s and 6s pattern. Shade the 3s and circle the 6s. a Show the 4s pattern. 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 91 92 93 94 95 96 97 98 99 100 dShade the 9s pattern, then put a circle around all the numbers 5 less than numbers ending in 9. c Show the 11s pattern. 1 2 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 91 92 93 94 95 96 97 98 99 100 Complete these number patterns by looking for skip counting patterns. a 6 12 18 24 30 36 42 48 b 9 18 27 36 45 54 63 72 c 32 28 24 20 16 12 8 4 Patterns and Algebra Copyright © 3P Learning Pty Ltd E 1 SERIES TOPIC 3 Patterns and functions – skip counting 3 Colour the skip counting pattern for 3s up to 30. If you kept going on a complete hundred grid, would 52 be coloured in? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 How can you tell without using a whole hundred grid? No, because 52 is not a multiple of 3. ____________________________________________________________________ 4 Only 3 numbers are shaded in each of the skip counting patterns below. Work out the pattern and complete the shading: a 1 2 3 4 5 6 8 9 b 10 1 2 3 4 5 6 8 7 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 91 92 93 94 95 96 97 98 99 100 This shows a skip counting pattern of: 5 7 This shows a skip counting pattern of: 4s 8s Shade these sequences on the hundred grid: Sequence 1: start at 1 and show a skip counting pattern of 11. Sequence 2: start at 1 and show a skip counting pattern of 9. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Patterns and Algebra Copyright © 3P Learning Pty Ltd E 1 SERIES TOPIC 4 Patterns and functions – completing and describing patterns So far we have looked at skip counting patterns that begin at zero. Here is a skip counting pattern of 5s that begins at 7. This pattern starts at 7. 7 The rule is: Add 5. 1 2 +5 17 +5 22 27 +5 +5 Continue the pattern from the starting number: a Add 10 11 21 31 41 51 61 71 81 b Add 5 55 60 65 70 75 80 85 90 c Subtract 4 40 36 32 28 24 20 16 12 Practise counting backwards by 10 and 100. Backwards by 10: 3 12 Backwards by 100: a 112 102 92 82 72 a 673 573 473 373 273 b 219 209 199 189 179 b 798 698 598 498 398 c 583 573 563 553 543 c 1 010 910 810 710 610 Look carefully at these number pattern grids. There are 4 rules: across, down, and along each diagonal. a 15 16 17 18 25 26 27 35 36 45 46 b 32 35 38 41 28 38 41 44 47 37 38 44 47 50 53 47 48 50 53 56 59 Patterns and Algebra Copyright © 3P Learning Pty Ltd E 1 SERIES TOPIC 5 Patterns and functions – completing and describing patterns 4 Figure out the missing numbers in each pattern and write the rule. a 72 63 54 45 36 b 27 –9 Rule: _________________________ c 44 49 54 64 59 81 73 65 57 49 41 –8 Rule: _________________________ d 69 +5 Rule: _________________________ 28 35 42 49 56 63 +7 Rule: _________________________ Some number patterns can be formed with 2 operations each time. For example: 2 ×2+3 ×2+3 7 17 ×2+3 37 The rule is to multiply by 2 and add 3 each time. 5 Complete these number patterns, by following the rules written in the diamond shapes. Describe the rule underneath. 3 +5x2 16 +5x2 42 +5x2 94 to add 5 and multiply by 2 each time. The rule is____________________________________________________________ 6 Roll a die to make the starting number. Continue the sequence by following the rule: a Rule: + 4 × 2 b Rule: + 1 × 3 c Rule: + 3 × 2 Answers will vary. Patterns and Algebra Copyright © 3P Learning Pty Ltd E 1 SERIES TOPIC 6 Patterns and functions – predicting repeating patterns When we use number patterns in tables, it can help us to predict what comes next. Look at the table below and how we can use it to predict the total number of sweets needed for any number of children at a party. This table shows us that 1 sweet bag contains 8 sweets and 2 bags contain 16 sweets. We can see that the rule for the pattern is to multiply the top row by 8 to get the bottom row each time. Number of sweet bags 1 2 3 4 5 10 Number of sweets 8 16 24 32 40 80 ×8 To find out how many sweets are in 10 bags, we don’t need to extend the table, we can just apply the rule. 10 × 8 = 80. So, 10 bags contain 80 sweets. This helps us plan how many sweets are needed for a party. 1 Complete the table for each problem: aTom receives $5 a week pocket money as long as he does all his chores. How much pocket money does Tom get after 10 weeks? Weeks 1 2 3 4 5 10 Pocket money 5 10 15 20 25 50 bA flower has 7 petals. How many petals are there in a bunch of 10 flowers? Flowers 1 2 3 4 5 10 Number of petals 7 14 21 28 35 70 cA flag has 6 stars. How many stars are there on 10 flags? Flags 1 2 3 4 5 10 Number of stars 6 12 18 24 30 60 dAt a pizza party, each person eats 3 pieces of pizza. How many pieces of pizza do 10 people eat? Guests 1 2 3 4 5 10 Pizza pieces 3 6 9 12 15 30 Patterns and Algebra Copyright © 3P Learning Pty Ltd E 1 SERIES TOPIC 7 Patterns and functions – predicting repeating patterns 2 Each of these kids wrote the first 3 numbers of a skip counting pattern of 6, starting at different numbers. Each kid’s sequence goes down the column. Imagine the sequence continues. Mel Brianna Brad Gen Jo Kate 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Kate a Who had the number 42 in their column?_ _______________________________ Brianna b Who had the number 50 in their column?_ _______________________________ 3 Look at each pattern of shapes and complete the table below: Repeat section 1 2 3 4 5 10 Number of circles 2 4 6 8 10 20 Number of triangles 1 2 3 4 5 10 aShow what this entire sequence would look like with 10 repeat sections: Look for the section that repeats. What is it made up of? This is the rule. Patterns and Algebra Copyright © 3P Learning Pty Ltd E 1 SERIES TOPIC 8 Patterns and functions – predicting growing patterns Number patterns in tables can help us with problems like this. Mia is making this sequence of shapes with matchsticks and wants to know how many she will need for 10 shapes. Shape 1 Shape 2 Shape 3 Shape number 1 2 3 4 5 10 Number of matchsticks 3 6 9 12 15 30 ×3 To find out how many matchsticks are needed for 10 triangles, we don’t need to extend the table, we can just apply the function rule: Number of matchsticks = Shape number × 3 1 Complete the table for each sequence of matchstick shapes and find the number of matchsticks needed for the 10th shape. a b c Shape 1 Shape 2 Shape 3 Shape number 1 2 3 4 5 10 Number of matchsticks 4 8 12 16 20 40 Shape 1 Shape 2 Shape 3 Shape number 1 2 3 4 5 10 Number of matchsticks 6 12 18 24 30 60 Shape 1 Shape 2 Shape 3 Shape number 1 2 3 4 5 10 Number of matchsticks 7 14 21 28 35 70 Patterns and Algebra Copyright © 3P Learning Pty Ltd E 1 SERIES TOPIC 9 Patterns and functions – predicting growing patterns 2 Look at these growing patterns. Complete the table and follow the rule to draw Picture 5: a Picture 1 Picture 2 l ll l Picture 4 Picture 5 l l lll l l l llll l l l l lllll Picture number 1 2 3 4 5 Number of dots 1 3 5 7 9 Rule b Picture 3 Picture number × 2 – 1 = Number of dots Picture 1 Picture 2 Picture number 1 2 3 4 5 Number of squares 4 6 8 10 12 Rule Picture 3 Picture 4 Picture 5 Picture number × 2 + 2 = Number of squares How many squares will Picture 8 have? 8 × 2 + 2 = 18 squares Patterns and Algebra Copyright © 3P Learning Pty Ltd E 1 SERIES TOPIC 10 Patterns and functions – function machines This is a function machine. IN Numbers go in, have the rule applied, and come out again. 2 OUT RULE: 6 ×3 8 24 10 1 Look carefully at the numbers going in these function machines and the numbers coming out. What is the rule? a b IN 5 8 RULE: ×3 9 2 OUT 15 IN 4 24 7 27 9 OUT 24 RULE: ×6 42 54 What numbers will come out of these function machines? b a IN 3 4 RULE: ×8 7 3 30 OUT 24 IN 24 32 48 56 72 OUT RULE: 3 ÷8 6 9 What numbers go in to these number function machines? a b IN 46 62 122 RULE: – 10 OUT 36 IN 68 52 277 112 112 Patterns and Algebra Copyright © 3P Learning Pty Ltd OUT 78 RULE: + 10 287 122 E 1 SERIES TOPIC 11 That’s my number! Getting ready What to do apply This is a game for 2 players. You will need some transparent counters each in 2 different colours and 2 dice. copy Player 1 rolls 2 dice. The first die shows the starting number and the second die shows the skip counting pattern. Player 1 writes down the first 4 numbers of their sequence. For example, if Player 1 rolls a 2 and a 6, the starting number is 2 and the rule is + 6. So Player 1 writes 2, 8, 14, 20 and chooses one of these numbers to cover with their counter. Player 2 has their turn, following the same steps as above. They choose one number to cover with their counter. If the number is already covered, they can’t put down a counter. The winner is the first player to have their counters in a group of 4 (2 × 2). 1 2 3 4 5 6 7 8 9 10 7 8 9 10 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 Patterns and Algebra Copyright © 3P Learning Pty Ltd E 1 SERIES TOPIC 12 Equations and equivalence – understanding equivalence Look at these balanced scales. On one side there is the sum 4 + 3 and on the other side there is a total of 7 triangles. This makes sense because it shows the equation 4 + 3 = 7. 4 + 3 Equation is another word for a sum. With equations, both sides must be equal. 1 4 + 3 = 7 Balance each set of scales by writing a number in the box that is equivalent to the total number of shapes. Then write the matching equation. 5 + 4 5 + 4 = 9 5 + 3 = 8 a 5 + 3 b 2 Balance each set of scales by writing a number in the box. Then write the matching equation. 30 + 55 85 30 + 55 = 85 45 + 55 100 45 + 55 = 100 a b Patterns and Algebra Copyright © 3P Learning Pty Ltd E 2 SERIES TOPIC 13 Equations and equivalence – not equal to symbol When two sides of an equation are not balanced, it means that they are not equal. To show that an equation is not equal, we use the not equals symbol like this: 1 + 12 ≠ 9 20 Write numbers in each box to show equations that are not balanced: a 50 b 70 45 65 + 65 200 + 50 70 ≠ ≠ 200 45 Answers will vary. c d 35 30 185 160 ≠ 185 35 + + 30 Answers will vary. 2 ≠ 160 Answers will vary. Complete the equations below by using only the numbers in the cards. Look carefully to see whether it is an = or ≠ symbol. 20 a 15 + 35 = 50 15 35 b or c 20 + 15 = 35 d or Patterns and Algebra Copyright © 3P Learning Pty Ltd 20 + 15 ≠ 50 20 + 35 ≠ 50 15 + 35 ≠ 35 20 + 35 ≠ 35 E 2 SERIES TOPIC 14 Equations and equivalence – greater than and less than When two sides of an equation are not balanced, one side is greater than the other. We can show this with greater than (>) and less than (<) symbols like this: 12 25 14 15 30 + 12 1 < 14 30 + 15 13 > 13 25 Complete the equations below by using only the numbers in the cards. Look carefully to see whether it is an > or < symbol. The first one has been done for you. a 18 22 b 50 35 25 50 18 + 22 50 35 + 25 50 18 c + 22 < 78 32 100 50 35 or or 50 50 d 100 + 25 > 107 83 200 + + 25 35 2 78 100 100 + + + 35 25 107 + 83 78 + 32 or or 50 > > 200 32 32 78 > > > 107 100 78 32 + < 83 200 Alex is older than Gilly but younger than Taylor. Their ages could be described as: 16 > 12 > 9 How old is each person? 12 Alex is ______ 9 Gilly is ______ Patterns and Algebra Copyright © 3P Learning Pty Ltd 16 Taylor is ______ E 2 SERIES TOPIC 15 Equations and equivalence – greater than and less than 3 Complete the number sentences below by writing numbers in the blank boxes: Answers will vary. a 4 38 + > 100 b 29 + + 257 d 500 < 1 000 f + < h + < c > e + > g + > 243 < 460 100 + 1 000 Sam and Will’s mother is When you add these amounts, look for trying to work out how much bonds to $1. For example: to budget for her children’s $1.40 + $1.60 = (40c + 60c) + $1 + $1 = $3 daily lunch orders. She is wondering if $50 is enough for both Sam and Will. Add up the cost of each child’s lunch order for the week and then complete a matching number sentence. Sam’s lunch orders Monday Tuesday Wednesday Thursday Friday $4.60 $5.40 $7.30 $3.70 $6 Will’s lunch orders Monday Tuesday Wednesday Thursday Friday $5.20 $3.80 $5.90 $6.10 $5 + $27 Sam’s total $26 > $50 Will’s total Patterns and Algebra Copyright © 3P Learning Pty Ltd E 2 SERIES TOPIC 16 Equations and equivalence – balanced equations using + and × There are 2 different equations we could write for one set of balanced scales. 8 1 8 8 24 8 + 8 + 8 = 3 × 8 = 24 24 Work out the values of the symbols in each problem: a b 9 9 9 9 9 7 7 7 7 7 7 45 5 × 9 = 45 42 6 × 7 = 42 63 7 × 9 = 63 42 6 × 7 = 42 c d Patterns and Algebra Copyright © 3P Learning Pty Ltd E 2 SERIES TOPIC 17 Equations and equivalence – balanced equations using + and × 2 Find the values of these symbols: a If is 5, what is the value of ? 2 b If is 8, what is the value of 5 = 5 = 2 = 6 = 4 × 2 × 4 × 12 = 12 × 2 = 2 ? 3 3 × × 8 Find the values of both symbols from the clues: a If both sides are equal to 36, what is the value of each symbol? 2 × 18 = 18 = 3 b If both sides are equal to 10, what is the value of each symbol? 2 Patterns and Algebra Copyright © 3P Learning Pty Ltd × 5 = 5 = 5 E 2 SERIES TOPIC 18 Equations and equivalence – using symbols for unknowns 1 Write an equation for these word problems. Write an equation using a unknown number. s for the aBec collects stickers. She has 48 bumper stickers, 12 glitter stickers and 15 smiley face stickers. How many stickers does Bec have in her collection? + 48 12 + 15 = s= s 75 bCharlie saved $5 a week of his pocket money over 8 weeks but then spent $15. How much did Charlie have at the end of 8 weeks? $5 × 8 – $15= s= s $25 c5 000 people are spectators at a football match. 2 700 are there to support Team A while the rest are there to support Team B. How many spectators support Team B? 5 000 – 2 700= 2 s= s 2 300 In this triangle, the numbers on the sides are the totals. So 10 + 25 30 15 = 30 Work out the value of the other symbols: 10 = 20 Patterns and Algebra Copyright © 3P Learning Pty Ltd = 5 E 2 SERIES TOPIC 19 Fruit values What to do solve Work out the value of each type of fruit: 37 = 11 = 15 = 9 = 10 = 2 = 11 = 16 = 11 = 1 45 33 35 39 41 14 33 22 15 23 31 18 38 33 48 13 28 Patterns and Algebra Copyright © 3P Learning Pty Ltd E 2 SERIES TOPIC 20 Mystery snacks What to do solve Work out what is the snack box from the clues. Clue 1 Clue 2 Hint: Keep the scale balanced by adding Crunchy O to each side in Clue 2. Then work out what else 2 packets of chips is equal to. From there, you can work out your answer. Patterns and Algebra Copyright © 3P Learning Pty Ltd E 2 SERIES TOPIC 21 Patterns and functions 1 Name___________________ Each child has 4 buttons on their school shirt. Complete the table to show how many buttons different amounts of children have. Number of children 1 Number of buttons 4 2 3 4 5 10 a How many buttons do 20 children have? b How did you work this out? __________________________________________________________________ 2 Complete these function machines. a b IN 6 7 RULE: OUT IN OUT 57 RULE: ×5 + 10 34 9 3 98 Complete the table for each sequence of matchstick shapes and find the number of matchsticks needed for 10th shape: Shape 1 Shape 2 Shape 3 Shape number 1 Number of matchsticks 6 2 Skills 3 4 Not yet 5 Kind of 10 Got it ompletes a shape or number pattern by following • C a function rule an write a rule to describe input and output • C relationships Series E Topic 1 Assessment Copyright © 3P Learning Pty Ltd 22 Patterns and functions 1 Name___________________ Each child has 4 buttons on their school shirt. Complete the table to show how many buttons different amounts of children have. Number of children 1 2 3 4 5 10 Number of buttons 4 8 12 16 20 80 a How many buttons do 20 children have? 80 b How did you work this out? Multiplied the number of children by 4. __________________________________________________________________ 2 Complete these function machines. a b IN 6 7 RULE: OUT IN 30 47 35 24 45 88 ×5 9 3 OUT 57 RULE: + 10 34 98 Complete the table for each sequence of matchstick shapes and find the number of matchsticks needed for 10th shape: Shape 1 Shape 2 Shape 3 Shape number 1 2 3 4 5 10 Number of matchsticks 6 12 18 24 30 60 Skills Not yet Kind of Got it ompletes a shape or number pattern by following • C a function rule an write a rule to describe input and output • C relationships Series E Topic 1 Assessment Copyright © 3P Learning Pty Ltd 23 Patterns and functions 4 Complete these number patterns by looking for skip counting patterns: a 7 28 72 b 5 Name___________________ 35 54 36 Colour the skip counting pattern for 4s up to 30. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 aIf you kept going on a complete hundred grid, would 54 be coloured in? Yes / No bHow can you tell without using a whole hundred grid? –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 6 Figure out the missing numbers each pattern and write the rule: a 56 49 35 b 28 Rule: _________________________ 7 30 36 42 Rule: _________________________ Complete a number sequence for each rule: Rules Sequences × 2 + 1 2 × 2 – 1 2 × 3 – 1 2 Skills Not yet Kind of Got it • Completes a skip counting pattern • Completes a number pattern and write the rule in words • Completes a number pattern with 2 operations Series E Topic 1 Assessment Copyright © 3P Learning Pty Ltd 24 Patterns and functions 4 5 Name___________________ Complete these number patterns by looking for skip counting patterns: a 7 14 21 28 35 42 49 56 b 81 72 63 54 45 36 27 18 Colour the skip counting pattern for 4s up to 30. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 aIf you kept going on a complete hundred grid, would 54 be coloured in? Yes / No bHow can you tell without using a whole hundred grid? 54 is not in the 4 times table. –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 6 Figure out the missing numbers each pattern and write the rule: a 56 49 42 35 28 b 21 –7 Rule: _________________________ 7 30 36 42 48 54 60 +6 Rule: _________________________ Complete a number sequence for each rule: Rules Sequences × 2 + 1 2 5 11 23 47 95 × 2 – 1 2 3 5 9 17 33 × 3 – 1 2 5 14 41 122 365 Skills Not yet Kind of Got it • Completes a skip counting pattern • Completes a number pattern and write the rule in words • Completes a number pattern with 2 operations Series E Topic 1 Assessment Copyright © 3P Learning Pty Ltd 25 Equations and equivalence 1 Complete this equation to show it on the balanced scales: 30 + 2 + 100 = Complete the number sentences below by writing numbers in the blank boxes: a 3 Name___________________ 25 + > 100 b 29 + < 100 Find the value of the symbol: a 42 = bMia saved $9 of her pocket money each week over 6 weeks but then spent $15. How much did she have at the end of 6 weeks? Write an equation using a symbol to represent the unknown and show your working in the space below: Skills Not yet Kind of Got it • Recognises that equals sign means equivalence • Recognises the greater than and less than symbol • Finds the value of a symbol Series E Topic 2 Assessment Copyright © 3P Learning Pty Ltd 26 Equations and equivalence 1 Complete this equation to show it on the balanced scales: 30 + 2 Name___________________ + 30 100 70 70 = 100 Complete the number sentences below by writing numbers in the blank boxes: Answers will vary. a 3 25 + > 100 b + 29 < 100 Find the value of the symbol: a = 42 7 bMia saved $9 of her pocket money each week over 6 weeks but then spent $15. How much did she have at the end of 6 weeks? Write an equation using a symbol to represent the unknown and show your working in the space below: ($9 × 6) – $15 = $54 – $15 = $39 = $39 * Choice of symbol will vary. Skills Not yet Kind of Got it • Recognises that equals sign means equivalence • Recognises the greater than and less than symbol • Finds the value of a symbol Series E Topic 2 Assessment Copyright © 3P Learning Pty Ltd 27 Series E – Patterns and Algebra Topic 1 Patterns and functions Topic 2 Equations and equivalence NSW PAS2.1 – Generates, describes and records number patterns using a variety of strategies and completes simple number sentences by calculating missing values • identifying and describing patterns when counting forwards or backwards by threes, fours, sixes, sevens, eights or nines • creating, with materials or a calculator, a variety of patterns using whole numbers • finding a higher term in a number pattern given the first five terms e.g. determine the 10th term given a number pattern beginning with 4, 8, 12, 16, 20, … • working through a process of building a simple geometric pattern involving multiples, completing a table of values, and describing the pattern in words PAS2.1 – Generates, describes and records number patterns using a variety of strategies and completes simple number sentences by calculating missing values • forming arrays using materials to demonstrate multiplication patterns and relationships • completing number sentences involving one operation by calculating missing values • applying the associative property of addition and multiplication to aid mental computation e.g. 2 + 3 + 8 = 2 + 8 + 3, 2 × 3 × 5 = 2 × 5 × 3 • using the equals sign to record equivalent number relationships and to mean ‘is the same as’ rather than as an indication to perform an operation e.g. 4 × 3 = 6 × 2 VIC Number VELS – Level 3 • at Level 3, students recognise the mathematical structure of problems and use appropriate strategies (for example, recognition of sameness, difference and repetition) to find solutions • students use calculators to explore number patterns and check the accuracy of estimations Number VELS – Level 3 • at Level 3, students recognise the mathematical structure of problems and use appropriate strategies (for example, recognition of sameness, difference and repetition) to find solutions PA 3.1 – Students create and continue number patterns, identify, describe and represent relationships between two quantities and use backtracking to reverse any one of the four operations • input → output (function machines) • number – rules based on previous term – calculators (whole and decimal numbers involving any operations) – missing term – non-patterns or patterns with errors – rules based on the position of terms (one operation only) • representations of relationships – rules, tables, graphs PA 3.2 – Students represent and describe equivalence in equations that involve combinations of multiplication and division or addition and subtraction • number – rules based on previous term – calculators (whole and decimal numbers involving any operations) – missing term – non-patterns or patterns with errors – rules based on the position of terms (one operation only) • equations (number sentences) • symbols – equals (=) – does not equal (≠) – greater than (>) – less than (<) – for unknowns (shapes, boxes, question marks, spaces, lines) Region QLD Series E Outcomes Copyright © 3P Learning Pty Ltd 28 Series E – Patterns and Algebra Region Topic 1 Patterns and functions Topic 2 Equations and equivalence SA 2.9 – Searches for, represents and analyses different forms of spatial and numerical patterns, and relates these to everyday life 2.10 – Represents and communicates patterns with everyday and mathematical language, including symbols, sketches, materials, number lines and graphs • represents and analyses different forms of patterns of number, shape and measurement drawn from everyday life • represents spatial patterns with tables, drawings and symbols WA N 6a.2 • reads, writes, says and counts with whole numbers to beyond 100, using them to compare collection sizes and describe order A 2 Algebra • complete either addition, subtraction, multiplication and division number sentences by calculating a missing number e.g. ___ + 8 = 17, 5 + 2 = __ + 3 • use the equal sign to mean ‘is the same as’, e.g. 4 + 3 = 2 + 5 NT A 2 Algebra • recognise and continue physical patterns formed by repeatedly adding or subtracting a predictably increasing or decreasing number of elements • express patterns as a number sequence • generate patterns and number sequences given a description or set of instructions • continue and complete number sequence patterns involving repeated addition or subtraction • complete equations involving simple addition or subtraction where one of the elements (addend, minuend or subtrahend) is missing • use words and tables to record relationships between pairs of numbers 18.LC.9 – inverse and equivalence relationships, including how inverse operations enable them to work out related number facts and solve unknown elements of simple equations involving addition and subtraction 18.LC.11 – equations (number sentences and models to represent mathematical problems and situations based around a single operation ACT 18.LC.1 – patterns in number and space (e.g. multiple copies of shapes tessellation) and the role that position plays in patterns 18.LC.4 – basic transformations (flips, slides and turns) of shapes and description of the changes that occur 18.LC.16 – represent and interpret patterns in number and space, identify the rules that describe the pattern, work out further elements and use materials to model and continue spatial patterns 18.LC.21 – recognise and describe relationships and represent them using concrete materials, drawings, lists, tables and some mathematical symbols 18.LC.22 – analyse simple relationships and make predictions based on the information they have Series E Outcomes Copyright © 3P Learning Pty Ltd 29 Series E – Patterns and Algebra Region TAS Topic 1 Patterns and functions Topic 2 Equations and equivalence Standards 2 - 3, Stages 4 - 8 • using objects, pictures and other symbols to represent problem situations • using number to describe patterns e.g. ‘My pattern is a counting by 6 pattern’, or ‘my pattern doubles each time’ • making and extending more sophisticated patterns with materials and with numbers e.g. using the constant function on a basic calculator to count by a given number and explore patterns or finding out what happens when we keep doubling numbers • exploring growth patterns in table form • creating and follow sequences of actions and instructions e.g. follow a set of instructions, follow a tourist guide, create ‘think of a number’ problems or a set of rules for a dice game • making predictions based on growth patterns e.g. simple match stick or block patterns • investigating patterns in the number system e.g. adding ten to a number, odd and even number investigations, patterns in multiplication and division Standards 2 - 3, Stages 4 - 8 • using equivalence to solve simple equations with unknowns e.g. 5 + 4 = + 2 • exploring situations where inverse operations can be applied and describe how inverse operations apply to other situations and problems e.g. interpret 13 = + 8 as a subtraction situation, use a 4 by 3 array to work out associated multiplication and division problems • identifying and describing relationships, such as inverses and equivalence in a variety of ways e.g. using balances to show that 14 + 8 can be changed to 12 + 10 without affecting the equivalence • identifying and describing relationships, such as inverses and equivalence in a variety of ways e.g. using balances to show that 14 + 8 can be changed to 12 + 10 without affecting the equivalence Series E Outcomes Copyright © 3P Learning Pty Ltd 30